Contents: Introduction; Feigenbaum: maps in one dimensions; Henon: maps in two dimensions; Hilbert: Differential equations in two dimensions; Lorentz: ODEs in higher dimensions; Birkhof: billiards; Hedlund: cellular automata; Mandelbrot: maps in the complex plane; Bernoulli: subshifts of finite type; Weyl: dynamical systems in number theory; Poincare: many body problems; Einstein: geodesic flows. Lecture Notes Collection FreeScience.info ID931 Obtained from... Topics: Dynamical Systems, "
Dynamical Systems with Applications using MATLAB® Author: Stephen Lynch Published by Birkhäuser Boston ISBN: 978-0-8176-4321-8 DOI: 10.1007/978-0-8176-8156-2 Table of Contents: A Tutorial Introduction to MATLAB and the Symbolic Math Toolbox Linear Discrete Dynamical Systems Nonlinear Discrete Dynamical Systems Complex Iterative Maps Electromagnetic Waves and Optical Resonators Fractals and Multifractals Controlling Chaos Differential Equations Planar Systems Interacting Species Limit Cycles... Topics: MATLAB, Differentiable dynamical systems
On Some Aspects of the Theory of Anosov Systems: With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows Author: Grigoriy A. Margulis Published by Springer Berlin Heidelberg ISBN: 978-3-642-07264-2 DOI: 10.1007/978-3-662-09070-1 Table of Contents: On Some Aspects of the Theory of Anosov Systems Periodic Orbits of Hyperbolic Flows Topics: Mathematics, Differentiable dynamical systems, Geometry, Differentiable dynamical systems,...
byVictor Cortiano, Marcelo Massao Kataoka Higaskino and William Hitoshi Tsunoda Meira
Two programs written in Processing for Ploting Fractals. License: GPL v3 or later; http://www.gnu.org/licenses/gpl-3.0.html For the Scientific Paper, see: http://www.archive.org/details/Utfpr-Fractalspt-br Topics: Fractals, Dynamical Systems, Software, Processing
Thus far, we have studied only classical attractors such as �xed points and limit cycles. In this lecture we begin our study of strange attractors. We emphasize their generic features. Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics Source: http://www.flooved.com/reader/1839
In this lecture we discuss the other two generic routes to chaos, intermittency and quasiperiodicity. Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics Source: http://www.flooved.com/reader/1838
In these lectures we derive (mostly) the equations of viscous �uid dynamics. We then show how they may be generalized to the problem of Rayleigh-Benard convection�the problem of a �uid heated from below. Later we show how the RB problem itself may be reduced to the famous Lorenz equations. The highlights of these lectures are as follows: � Navier-Stokes equations of �uid dynamics (mass and momentum conser_vation). � Reynolds number � Phenomenology of RB convection � Rayleigh... Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics Source: http://www.flooved.com/reader/1832
The chaotic phenomena of the Lorenz equations may be exhibited by even simpler systems. Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics Source: http://www.flooved.com/reader/1837
In this lecture we point broadly sketch some of the mathematical issues con_cerning Lyaponov exponents. We also brie�y describe how they are com_puted. We then conclude with a description of a simple model that shows how both fractals and Lyaponov exponents manifest themselves in a simple model. Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics Source: http://www.flooved.com/reader/1828
We are interested in the analysis of experimental (or numerical) data, which is almost always discrete. Thus we specialize to discrete Fourier transforms. Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics Source: http://www.flooved.com/reader/1834
Poincare's work on the three-body problem later became the framework for studying chaotic systems. Since then, mathematicians have made progress in these and other dynamical systems. On this program, Mason Porter talked about exciting developments in this field. Travis Heime also discussed condensed matter physics. Topics: science, chaos theory, dynamical systems, condensed matter Source: Groks Science Radio Show Podcast
Thus we seek a geometric depiction of the trajectories in a lower-dimensional space�in essence, a view of phase space without all the detail. Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics Source: http://www.flooved.com/reader/1845
We now proceed to quantify the �strangeness� of strange attractors. There are two processes of interest, each associated with a measurable quantity: � sensitivity to initial conditions, quanti�ed by Lyaponov exponents. � repetitive folding of attractors, quanti�ed by the fractal dimension. Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics Source: http://www.flooved.com/reader/1835
Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb. Topics: Differentiable dynamical systems, Iterative methods (Mathematics) Source: http://books.google.com/books?id=QbwTAAAAYAAJ&oe=UTF-8
Summary Finally, we summarize the characteristics of dissipative systems: � Energy not conserved. � Irreversible. � Contraction of areas (volumes) in phase space. Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics Source: http://www.flooved.com/reader/1830
To introduce dynamical systems, we begin with one of the simplest: a free oscillator. Speci�cally, we consider an unforced, undamped pendulum. Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics Source: http://www.flooved.com/reader/1842
The Statistical Dynamics of Turbulence Author: Dr. Jovan Jovanović Published by Springer Berlin Heidelberg ISBN: 978-3-642-05793-9 DOI: 10.1007/978-3-662-10411-8 Table of Contents: Some historical notes on the statistical dynamics of turbulence Dynamic equations for moments Dynamics of the turbulent dissipation rate Velocity-pressure gradient correlations Turbulent transport Topics: Engineering, Differentiable dynamical systems, Vibration, Hydraulic engineering, Differentiable...
In the beginning of the Twentieth Century Poincare recurrence theorem revolutionized modern theory of dynamical systems and statistical mechanics. Indeed, the problem of recurrence times lies in the very essence of discrete mathematics and statistical mechanics. The meaning of the theorem is that distant parts of the phase space repeatedly visited by the trajectory of the dynamical system possessing some ergodic properties, an argument used by Zermelo against Boltzmann. For very small cells of... Topics: Dynamical systems, Poincare recurrence theorem, recurrence times, logistic map, ergodicity
Symmetry and Perturbation Theory in Nonlinear Dynamics Author: Giampaolo Cicogna, Giuseppe Gaeta Published by Springer Berlin Heidelberg ISBN: 978-3-540-65904-4 DOI: 10.1007/3-540-48874-X Table of Contents: Introduction Symmetry and Differential Equations Dynamical Systems Symmetries of Dynamical Systems Normal Forms and Symmetries for Dynamical Systems Normal Forms and Symmetries for Hamiltonian Systems Convergence of the Normalizing Transformations Invariant Manifolds Further Normalization... Topics: Differentiable dynamical systems, Normal forms (Mathematics), Symmetry (Physics), Perturbation...
Bifurcation Theory: An Introduction with Applications to PDEs Author: Hansjörg Kielhöfer Published by Springer New York ISBN: 978-1-4684-9380-1 DOI: 10.1007/b97365 Table of Contents: Introduction Local Theory Global Theory Applications Topics: Applications of Mathematics, Differentiable dynamical systems, Differential equations, Partial,...
byBandt, Christoph; Mosco, U. (Umberto); Zähle, Martina
Fractal Geometry and Stochastics III Author: Christoph Bandt, Umberto Mosco, Martina Zähle Published by Birkhäuser Basel ISBN: 978-3-0348-9612-2 DOI: 10.1007/978-3-0348-7891-3 Table of Contents: Markov Operators and Semifractals On Various Multifractal Spectra One-Dimensional Moran Sets and the Spectrum of Schrödinger Operators Small-scale Structure via Flows Hausdorff Dimension of Hyperbolic Attractors in ℝ3 The Exponent of Convergence of Kleinian Groups; on a Theorem of Bishop and Jones... Topics: Mathematics, Differentiable dynamical systems, Mathematical optimization, Distribution (Probability...
Dynamics of Foliations, Groups and Pseudogroups Author: Paweł Walcza Published by Birkhäuser Basel ISBN: 978-3-0348-9611-5 DOI: 10.1007/978-3-0348-7887-6 Table of Contents: Dynamical systems Growth Entropy Invariant measures Hausdorff dimension Varia Topics: Mathematics, Group theory, Topological groups, Differentiable dynamical systems, Global...
byInternational Symposium on Acoustical Imaging (27th : 2003 : Saarbrücken, Germany); Arnold, W; Hirsekorn, S
Acoustical Imaging Author: W. Arnold, S. Hirsekorn Published by Springer Netherlands ISBN: 978-90-481-6652-7 DOI: 10.1007/978-1-4020-2402-3 Table of Contents: Micromachined Ultrasonic Transducers and Their use for 2D and 3D Imaging Portable Ultrasonic Phased Array System A Novel Approach for Ultrasonic Imaging of Sheet Contours for Hydroforming A Phased Array System for the Acquisition of Ultrasonic RF-Data up to 20 MHZ Computation and Properties of the Wide-Band Beam Pattern A Fine Pitch... Topics: Acoustic imaging, Vibration, Dynamical Systems, Control, Ultrasound, Characterization and...
Regularity Theory for Mean Curvature Flow Author: Klaus Ecker Published by Birkhäuser Boston ISBN: 978-0-8176-3781-1 DOI: 10.1007/978-0-8176-8210-1 Table of Contents: Introduction Special Solutions and Global Behaviour Local Estimates via the Maximum Principle Integral Estimates and Monotonicity Formulas Regularity Theory at the First Singular Time Topics: Global differential geometry, Differential equations, Parabolic, Flows (Differentiable dynamical...
Parametric cost analysis is a mathematical approach to estimating cost. Parametric cost analysis uses non-cost parameters, such as quality characteristics, to estimate the cost to bring forth, sustain, and retire a product. This paper reviews parametric cost analysis and shows how it can be used within the cost deployment process. Topics: FLIGHT CHARACTERISTICS, DYNAMICAL SYSTEMS, NUMERICAL ANALYSIS, AERODYNAMIC CHARACTERISTICS,...